simplify the expression 5²+253°-2³
Answers
Answer:
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(ii)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(iii)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(iv)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(v)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(vi)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(vii)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(viii)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(ix)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
(x)
The given expression is .
The formula of exponent to simplify the given expression is,
Now, simplify the given expression.
Thus, the value of is .
Question 2
Simplify and express each of the following in exponential form: (i) (2³ X 3⁴ X 4 )/ (3 X 32) (ii) ( (5 ²) ³ X 5⁴) ÷ 5 ⁷ (iii) 25⁴ ÷ 5³ (iv) ( 3 X 7² X 11⁸) / (21 x 11³) (v) 3⁷ / 3⁴ X 3³ (vi) 2° + 3° + 4° (vii) 2° × 3°× 4° (viii) (3° + 2°) × 5° (ix) (2 ² X a ⁵)/ (4³ X a³) (x)(a ⁵/a ³) X a⁸ (xi)( 4 ⁵ X a ⁸ b³)/(4 ⁵ X a ⁵b³) (xii)(2 ³ X 2)²
Answer:
(i)
The given the expression is .
Now, simplify the given expression.
Further simplify the above expression.
Thus, the value of given expression is .
(ii)
The given the expression is .
Now, simplify the given expression.
Further simplify the above expression.
Thus, the value of given expression is .
(iii)
The given the expression is .
Now, simplify the given expression.
Thus, the value of given expression is .
(iv)
The given the expression is .
Now, simplify the given expression.
Further simplify the above expression.
Thus, the value of given expression is .
(v)
The given the expression is .
Now, simplify the given expression.
Further simplify the above expression.
Thus, the value of given expression is .
(vi)
The given expression is .
Now, simplify the given expression.
Thus, the value of given expression is .
(vii)
The given expression is .
Now, simplify the given expression.
Thus, the value of given expression is .
(viii)
The given expression is .
Now, simplify the given expression.
Thus, the value of given expression is .
(ix)
The given the expression is .
Now, simplify the given expression.
Further simplify the above expression.
Thus, the value of given expression is .
(x)
The given the expression is .
Now, simplify the given expression.
Thus, the value of given expression is .
(xi)
The given the expression is .
Now, simplify the given expression.
Thus, the value of given expression is .
(xii)
The given expression is .
Now, simplify the given expression.
Thus, the value of given expression is .
Question 3
Say true or false and justify your answer: (i) 10 × 10¹¹ = 10011 (ii) 2³ > 5² (iii) 2³ × 3² = 6⁵ (iv) 3° = (1000)°
Answer:
(i)
The given statement is .
Now, simplify the L.H.S.
Similarly simplify the R.H.S.
Thus, the statement is false.
(ii)
The given statement is .
Now, simplify the L.H.S.
Similarly simplify the R.H.S.
L.H.S is not greater than R.H.S.
Thus, the statement is false.
(iii)
The given statement is .
Now, simplify the L.H.S.
Similarly simplify the R.H.S.
Thus, the statement is false.
(iv)
The given statement is .
Now, simplify the L.H.S.
Similarly simplify the R.H.S.
Thus, the statement is true.
Question 4
Express each of the following as a product of prime factors only in exponential form: (i) 108 × 192 (ii) 270 (iii) 729 × 64 (iv) 768
Answer:
(i)
Given, .
Factorise the given numbers as a product of prime factors.
Thus, the prime factors is .
(ii)
The given number is .
Factorise the given numbers as a product of prime factors.
Thus, the prime factors is .
(iii)
Given, .
Factorise the given numbers as a product of prime factors.
Thus, the prime factors is .
(iv)
The given number is .
Factorise the given numbers as a product of prime factors.
Thus, the prime factor is .
Question 5
Simplify: (i)( (2 ⁵)² X 7 ³)/ (8 ³ X 7) (ii)2(5 X 5 ² X t ⁸)/(10 ³ X t ⁴) (iii)( 3⁵ X 10⁵ X 25 )/(5⁷ X 6⁵)
Answer:
(i)
The given exponent is .
Further simplify the above exponent.
Thus, the value of given exponent is .
(ii)
The given exponent is .
Thus, the value of given exponent is .
(iii)
The given exponent is .
Further simplify the above exponent.
Thus, the value of given exponent is 1.