Question

Explain the error in the work shown. Find the correct answer.

Answer 1

The bases were not the same when the exponents were set equal to each other.

16 should have been written as 4 squared.

The exponent on the right should be 4a instead of 8a.

The correct solution is a=-3/4.

Answer 2

Answer:

$a=-\frac{3}{4}$

Step-by-step explanation:

We have to find the error in the given work.

$\frac{1}{64}=(16)^{2a}$

Reason: Given

$\frac{1}{(4)^3}=((2)^4)^{2a}$

$\frac{1}{a^x}=a^{-x}$

Using the property then we get

$4^{-3}=((2)^4)^{2a}$

$4^{-3}=2^{8a}$ By the property ($(a^x)^y=a^{xy}$)

$((2)^2)^{-3}=2^{8a}$

$2^{-6}=2^{8a}$

When bases are equal then power will be equal

Therefore, $8a=-6$

$a=\frac{-6}{8}=-\frac{3}{4}$

But in given work bases are not same but he wrote power equal.

This is the error in given work.He wrote $4^{-3}$ instead of $2^{-6}$