Question

part two: simplify the following expressions. show your work to receive full credit.
(5) $(2cdot 3)^4$
(6) $(7^3)^5$
(7) $3^3cdot 3^4$
(8) $\frac{x^{11}}{x^7}$

Explanation:

Step1: Simplify inside parentheses first

$2 \cdot 3 = 6$

Step2: Raise to the 4th power

$6^4 = 6 \times 6 \times 6 \times 6 = 1296$

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Step1: Apply power of a power rule

$(7^3)^2 = 7^{3 \times 2}$

Step2: Calculate the exponent

$7^6 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 = 117649$

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Step1: Apply product of powers rule

$3^3 \cdot 3^4 = 3^{3+4}$

Step2: Calculate the exponent

$3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187$

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Step1: Apply quotient of powers rule

$\frac{y^{10}}{y^7} = y^{10-7}$

Step2: Simplify the exponent

$y^3$

Answer:

[5] $\boldsymbol{1296}$
[6] $\boldsymbol{117649}$
[7] $\boldsymbol{2187}$
[8] $\boldsymbol{y^3}$