Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Express your answer using positive exponents. $\newline$ $\frac{3g^6}{3g^5}$

View step-by-step help

View step-by-step help

Multiply powers: variable bases

Full solution

Q. Simplify. Express your answer using positive exponents.

\newline

\frac{3g^6}{3g^5}

Identify Base and Operation: Identify the common base and the operation involved. $\newline$ We are dividing two expressions with the same base $g$ , and we need to simplify the expression using the laws of exponents.
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ The quotient rule states that when dividing powers with the same base, we subtract the exponents. $\newline$ $\frac{3g^6}{3g^5} = \frac{3}{3} \times g^{(6-5)}$
Simplify Coefficients and Powers: Simplify the coefficients and the powers of $g$ . $\newline$ $\frac{3}{3} = 1$ and $g^{6-5} = g^1$ $\newline$ So, $\frac{3g^6}{3g^5} = 1 \times g^1$
Recognize Exponent Rule: Recognize that $g^1$ is simply $g$ . Since any number to the power of $1$ is itself, we have $g^1 = g$ . Therefore, $1 \times g^1 = g$
Write Final Expression: Write the final simplified expression. $\newline$ The expression $\frac{3g^6}{3g^5}$ simplifies to $g$ .

More problems from Multiply powers: variable bases

Question

Factor completely.

\newline

2 x^{4}+4 x^{3}-30 x^{2}=

Posted 10 months ago

Question

Factor completely.

\newline

7 x^{5}-21 x^{4}+14 x^{3}=

Posted 10 months ago

Question

Divide. Write the quotient in lowest terms.

\newline

12 \div 1 \frac{1}{5}=

Posted 10 months ago

Question

Divide. Write the quotient in lowest terms.

\newline

5 \div 3 \frac{1}{3}=

Posted 10 months ago

Question

Divide. Write the quotient in lowest terms.

\newline

8 \div 1 \frac{4}{5}=

Posted 10 months ago

Question

Evaluate the following expression.

\newline

40 \cdot 8-10^{2}=

Posted 10 months ago

Question

Evaluate the following expression.

\newline

9+6^{2}-2 \cdot 8=

Posted 10 months ago

Question

Evaluate the expression. Do not round your answer.

\newline

(3+2)^{2}-7=

Posted 10 months ago

Question

Evaluate the expression.

\newline

Do not round your answer.

\newline

(4+3)^{2}+5=

Posted 10 months ago

Question

Evaluate the following expression.

\newline

3^{3}-10+7=

Posted 10 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant