Question

Write (8a^-3)^-4/3 in simplest form. Please show your work!

Answer 1

Answer:

(a/2) ^4  or a^4/16

Step-by-step explanation:

(8a^-3)^-4/3

split into two parts

8^ -4/3   *  (a^-3)^-4/3

using the power to the power rule we can multiply the exponents

8^(-4/3)  *a^(-3*-4/3)

8^ (-4/3) * a^(4)

replace 8 with 2^3

(2^3)^(-4/3) * a^(4)

using the power to the power rule we can multiply the exponents

2^(3*-4/3) * a^(4)

2 ^ (-4) * a^4

the negative exponent means it goes in the denominator if it is in the numerator

a^4/2^4

make a fraction

(a/2) ^4

or a^2/16

Answer 2

Answer:

$\frac{a^4}{16}$

Step-by-step explanation:

$(8a^{-3})^\frac{-4}{3}$

To simplify it we apply exponential property

(a^m)^n= a^mn

we multiply the inside exponent with outside exponent

8 or 8^1  are same

$(8^1a^{-3})^\frac{-4}{3}$

$(8^{1 \cdot \frac{-4}{3}}a^{-3 \cdot \frac{-4}{3}})$

When we multiply the exponents we get

$8^{\frac{-4}{3}}a^{4}$

8 can be written as 2 times 2 times 2 is 2^3

$2^{3 \cdot {\frac{-4}{3}}}a^{4}$

$2^{-4}a^4$

Now to make exponent positive move a^-4 to the denominator

$\frac{a^4}{2^4}$

$\frac{a^4}{16}$