### Instruction: What is $\left(\dfrac{3}{4}\right)^5$?### Response: To find $\left(\dfrac{3}{4}\right)^5$, I need to multiply the fraction by itself five times.
I can use the exponent rule for fractions, which says that $\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}$, to simplify the calculation.
So, $\left(\dfrac{3}{4}\right)^5=\dfrac{3^5}{4^5}$, and I just need to find the powers of 3 and 4.
I can use repeated squaring to find the powers quickly.
For example, $3^2=9$, $3^4=(3^2)^2=9^2=81$, and $3^5=3\cdot 3^4=3\cdot 81=243$.
Similarly, $4^2=16$, $4^4=(4^2)^2=16^2=256$, and $4^5=4\cdot 4^4=4\cdot 256=1024$.
Now I have $\left(\dfrac{3}{4}\right)^5=\dfrac{243}{1024}$, which is the exact answer.
If I want to write it as a decimal, I can divide 243 by 1024 using long division or a calculator.
I get about 0.237.