Question

1. m4 15 lesson 5

for problems 6–11, write each expression in expanded form.

1. $7^2$
2. $4^3$
3. $1^5$
4. $8^2$
5. $3 \cdot 4^2$
6. $5^3 \cdot 10$

for problems 12–17, write each expression by using exponential notation.

1. $5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$
2. $3 \cdot 3$
3. $10 \cdot 10 \cdot 10 \cdot 10$
4. $7 \cdot 7 \cdot 7 \cdot 7 \cdot 7$
5. $9 \cdot 9 \cdot 9 \cdot 4 \cdot 4$
6. $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3$

1. the prime factorization of 50 is $5 \cdot 2 \cdot 5$. use exponents to rewrite the expression.
2. write the prime factorization of 100 by using exponential notation.

Explanation:

Problem 6: \(7^2\)

Step1: Recall exponent definition

An exponent \(a^n\) means \(a\) multiplied by itself \(n\) times. Here, base is \(7\), exponent is \(2\).

Step2: Expand the expression

\(7^2 = 7\times7\)

Step1: Recall exponent definition

For \(a^n\), \(a\) is base, \(n\) is exponent (number of multiplications). Here, base \(4\), exponent \(3\).

Step2: Expand the expression

\(4^3=4\times4\times4\)

Step1: Recall exponent definition

\(a^n\) is \(a\) multiplied \(n\) times. Base \(1\), exponent \(5\).

Step2: Expand the expression

\(1^5 = 1\times1\times1\times1\times1\)

Answer:

\(7\times7\)

Problem 7: \(4^3\)