Math  /  Algebra

QuestionSimplify using the quotient rule, if possible. b9b5\frac{b^{9}}{b^{5}} your cnoice. A. b9b5=\frac{b^{9}}{b^{5}}= \square (Type expunential notation with positive exponents.) B. The expression cannot be simpli

Studdy Solution

STEP 1

1. The expression involves a quotient of powers with the same base.
2. The quotient rule for exponents can be applied here.
3. The base b b is non-zero.

STEP 2

1. Apply the quotient rule for exponents.
2. Simplify the expression.

STEP 3

Apply the quotient rule for exponents, which states that aman=amn\frac{a^m}{a^n} = a^{m-n} for any non-zero base a a .
b9b5=b95 \frac{b^9}{b^5} = b^{9-5}

STEP 4

Simplify the exponent:
95=4 9 - 5 = 4
Thus, the expression simplifies to:
b4 b^4
The simplified expression is:
b4 \boxed{b^4}

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