Question

Evaluate :- [7{(8)^ ⅓ +(125) ^⅓}^2]⅓

Answer 1

Answer:

Solution :

${ = {\Bigg[ 7\bigg\{{(8)}^{\frac{1}{3}} + {(125)}^{\frac{1}{3} }\bigg\}^{2} \Bigg]^{\frac{1}{3}}}}$

${ = {\Bigg[ 7\bigg\{{({2}^{3})}^{\frac{1}{3}} + {({5}^{3})}^{\frac{1}{3} }\bigg\}^{2} \Bigg]^{\frac{1}{3}}}}$

Using law of exponent rule to continuously evaluating the equation : (aᵐ)ⁿ = aᵐⁿ

${ = {\Bigg[ 7\bigg\{{({2})}^{3 \times \frac{1}{3}} + {({5})}^{3 \times \frac{1}{3} }\bigg\}^{2} \Bigg]^{\frac{1}{3}}}}$

${ = {\Bigg[ 7\bigg\{{({2})}^{\cancel{3} \times \frac{1}{\cancel{3}}} + {({5})}^{\cancel{3} \times \frac{1}{\cancel{3}}}\bigg\}^{2} \Bigg]^{\frac{1}{3}}}}$

${ = {\Bigg[ 7\bigg\{2 + 5\bigg\}^{2} \Bigg]^{\frac{1}{3}}}}$

${ = {\Bigg[ 7\bigg\{ \: \: 7 \: \: \bigg\}^{2} \Bigg]^{\frac{1}{3}}}}$

${ = {\Bigg[ 7\bigg\{ \: 7 \times 7 \: \bigg\} \Bigg]^{\frac{1}{3}}}}$

${ = {\Bigg[ 7 \times 7 \times 7\Bigg]^{\frac{1}{3}}}}$

${ = {\Big[ \: \: {7}^{3} \: \: \Big]^{\frac{1}{3}}}}$

Again using law of exponent rule to continuously evaluating the equation : (aᵐ)ⁿ = aᵐⁿ

${ = {\Big[ \: \: {7} \: \: \Big]^{3 \times \frac{1}{3}}}}$

${ = {\Big[ \: \: {7} \: \: \Big]^{\cancel{3} \times \frac{1}{\cancel{3}}}}}$

${ = {\Big[ \: \: {7} \: \: \Big]^{1}}}$

${={\sf{\underline{\underline{\pink{Ans = 7 }}}}}}$

Hence, the answer is 7.

$\pink{▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬}$

Answer 2

Answer:

Answer:

Exponent is defined as the method of expressing large numbers in terms of powers. Exponent defines the number of times a number multiplied by itself. The power is an expression that shows repeated multiplication of the same number or factor.

Exponent Laws

am . an = am+n

(am)n = amn

(ab)n = an bn

(a/b)n = an/bn

am/an = am-n

am/an = 1/an-m

Need to find:

We have to find the value of 125-1/3

Solution:

We know that 125 can be expressed in the power of 5

125 = 5 × 5 × 5

125 = 53

Hence the given number becomes

125 = 53(-1/3)

=5-1

= 1/5

Answer

125-1/3= 1/5

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Step-by-step explanation:

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