Question

for problems 16 - 19, use your knowledge of squares and cubes to fill in the boxes

1. $6^2 = \boxed{36}$
2. $6^{\square} = 216$
3. $\square^3 = 125$
4. $\square^2 = 16$

Explanation:

Problem 16: \( 6^2 = \square \)

Step 1: Recall the exponent rule

The expression \( 6^2 \) means multiplying 6 by itself, i.e., \( 6\times6 \).

Step 2: Calculate the product

\( 6\times6 = 36 \)

Step 1: Recall the exponent rule

We know that \( 6\times6\times6 = 216 \), and \( 6\times6\times6 \) can be written as \( 6^3 \).

Step 2: Determine the exponent

So the exponent that makes \( 6^{\square} = 216 \) is 3.

Step 1: Recall the cube root concept

We need to find a number \( x \) such that \( x\times x\times x = 125 \).

Step 2: Find the number

We know that \( 5\times5\times5 = 125 \), so the number is 5.

Answer:

36

Problem 17: \( 6^{\square} = 216 \)