Simplify ((-3/4)^5)^2

${({(- \frac{3}{4})}^{5})}^{2}$

Step 1

Multiply the exponents in ${({(- \frac{3}{4})}^{5})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(- \frac{3}{4})}^{5 \cdot 2}$

Multiply $5$ by $2$ .

${(- \frac{3}{4})}^{10}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{3}{4}$ .

${(- 1)}^{10} {(\frac{3}{4})}^{10}$

Apply the product rule to $\frac{3}{4}$ .

${(- 1)}^{10} \frac{3^{10}}{4^{10}}$

Step 3

Raise $- 1$ to the power of $10$ .

$1 \frac{3^{10}}{4^{10}}$

Step 4

Multiply $\frac{3^{10}}{4^{10}}$ by $1$ .

$\frac{3^{10}}{4^{10}}$

Step 5

Raise $3$ to the power of $10$ .

$\frac{59049}{4^{10}}$

Step 6

Raise $4$ to the power of $10$ .

$\frac{59049}{1048576}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{59049}{1048576}$

Decimal Form:

$0.05631351 \dots$