Question

Simplify the following;

(0.008)^power4/3

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

$\frac{16}{10000}$ this is the required value of  $(0.008)^{\frac{4}{3} }$

Step-by-step explanation:

Explanation:

Given that, (0.008)^power4/3

This can be written as, $(0.008)^{\frac{4}{3} }$

Now, $(0.008)^{\frac{4}{3} }$ = $(\frac{8}{1000} )^{\frac{4}{3} }$

⇒ $[(\frac{2}{10})^3}]^{\frac{4}{3} }$

• When multiplying a number by itself repeatedly, exponents are employed to illustrate this. For instance, $7^3$ can be used to represent 7 x 7 x 7.

• $(a^m)^n = a^{mn}$is the power rule for exponents. Multiply the exponent by the power to raise a number with an exponent to that power.

• For example, $(2^3)^4$ can be written as, $(2)^{2.4}$ = $(2)^8$

Therefore, we have,$[(\frac{2}{10})^3}]^{\frac{4}{3} }$

On comparing it from $(a^m)^n$

m = 3 and n = $\frac{4}{3}$ and a = $\frac{2}{10}$

Now, according to the power of the exponent rule

⇒ $[(\frac{2}{10})^3}]^{\frac{4}{3} }$ = $(\frac{2}{10})^{3.\frac{4}{3} }$ = $(\frac{2}{10})^4$ = $\frac{16}{10000}$

Final answer:

Hence, $\frac{16}{10000}$ this is the required answer.

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