Simplify the following leaving your answer in index form: a) 23x x 22x b) 26 / 23 c) (32 × 35)/(33)

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Here are the simplified expressions: 9. Simplify the following leaving your answer in index form a) 2^(3x) × 2^(2x) Step 1: Apply the rule for multiplying exponents with the same base, a^m × aⁿ = a^(m+n). 2^(3x) × 2^(2x) = 2^(3x+2x) Step 2: Add the exponents. = 2^(5x) The simplified expression is 2^(5x). b) 2⁶ ÷ 2³ Step 1: Apply the rule for dividing exponents with the same base, a^m ÷ aⁿ = a^(m−n). 2⁶ ÷ 2³ = 2⁶⁻³ Step 2: Subtract the exponents. = 2³ The simplified expression is 2³. c) (3² × 3⁵)/(3³) Step 1: Simplify the numerator using the rule a^m × aⁿ = a^(m+n). (3² × 3⁵)/(3³) = (3²⁺⁵)/(3³); = (3⁷)/(3³); Step 2: Apply the rule for dividing exponents with the same base, a^m ÷ aⁿ = a^(m−n). = 3⁷⁻³; = 3⁴ The simplified expression is 3⁴.

Simplify the following leaving your answer in index form: a) 23x x 22x b) 26 / 23 c) (32 x 35)/(33)

Answers

Step-by-step solution

Part a· 2 steps

Apply the rule for multiplying exponents with the same base, $a^m \times a^n = a^{m+n}$ .

Add the exponents.

Part b· 2 steps
$2^3$

Apply the rule for dividing exponents with the same base, $a^m \div a^n = a^{m-n}$ .

Subtract the exponents.

Part c· 2 steps
$3^4$

Simplify the numerator using the rule $a^m \times a^n = a^{m+n}$ .

Apply the rule for dividing exponents with the same base, $a^m \div a^n = a^{m-n}$ .

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Simplify the following leaving your answer in index form: a) 23x x 22x b) 26 / 23 c) (32 x 35)/(33)

Answers

Step-by-step solution

Part a· 2 steps

Apply the rule for multiplying exponents with the same base, am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Add the exponents.

Part b· 2 steps232^323

Apply the rule for dividing exponents with the same base, am÷an=am−na^m \div a^n = a^{m-n}am÷an=am−n.

Subtract the exponents.

Part c· 2 steps343^434

Simplify the numerator using the rule am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Apply the rule for dividing exponents with the same base, am÷an=am−na^m \div a^n = a^{m-n}am÷an=am−n.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Apply the rule for multiplying exponents with the same base, $a^m \times a^n = a^{m+n}$ .

Part b· 2 steps
$2^3$

Apply the rule for dividing exponents with the same base, $a^m \div a^n = a^{m-n}$ .

Part c· 2 steps
$3^4$

Simplify the numerator using the rule $a^m \times a^n = a^{m+n}$ .

Apply the rule for dividing exponents with the same base, $a^m \div a^n = a^{m-n}$ .