Question

power and exponents​

Answer 1

$\huge\mathcal\pink{Answer:}$

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$\huge{Powers\ and\ exponents}$

We know how to calculate the expression 5 x 5.
This expression can be written in a shorter way using something called exponents.

5 × 5

= 5²

An expression that represents repeated multiplication of the same factor is called a power.

The number 5 is called the base, and the number 2 is called the exponent.
The exponent corresponds to the number of times the base is used as a factor.

Here are some examples :-

3¹

3 to the first power3

4²

4 to the second power or 4 squared

4 × 4

5³

5 to the third power or 5 cubed

5 × 5 × 5

2^6

2 to the power of six

=2 × 2 × 2 × 2 × 2 × 2

$\huge{Multiplication}$

If two powers have the same base then we can multiply the powers. When we multiply two powers we add their exponents.

The rule:

x^a × x^b

= x^a+b

Examples :

4² + 4²

= 4²+²

= 4 ⁴

$\huge{Division}$

If two powers have the same base then we can divide the powers. When we divide powers we subtract their exponents.

The rule :

x⁴/x²

= x⁴-²

= x²

Example :

5⁴/5²

= 5⁴-²

= 5²

A negative exponent is the same as the reciprocal of the positive exponent.

x^-a

= 1/x^a

Example :

(4)-²

= 1/4²

When you raise a product to a power you raise each factor with a power.

(x × y)^a

Example :

(2x)⁴

= 2⁴ × 6⁴

= 16x⁴

The rule for the power of a power and the power of a product can be combined into the following rule :

( x^a × y^b )^z = x^a×z × y^b×z

Example :

(x² × y²)³

= x²×³ × x²×³

x^6 × x^6

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$\huge{Thankyou}$

Answer 2

Answer:

An expression that represents repeated multiplication of the same factor is called apower. The number 5 is called the base, and the number 2 is called the exponent. The exponentcorresponds to the number of times the base is used as a factor.