Question

1. $(2x^5)^4$
2. $(2x^{18})^7$
3. $(3n^8)^3$
4. $(3x^4)^3$
5. $(3b^8)^2$
6. $(m^9n^3)^3$
7. $(x^8y^5)^{10}$
8. $(yx^8)^3$
9. $(x^8y^5)^8$
10. $(3xy^8)^4$
11. $(2n^7v^{5.5})^5$
12. $(3a^{10}b^4)^3$

Explanation:

Problem 7: $(2x^5)^4$

Step1: Apply power of a product rule

$(2)^4 \cdot (x^5)^4$

Step2: Simplify constants and exponents

$16 \cdot x^{5 \times 4} = 16x^{20}$

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Problem 8: $(2x^8)^7$

Step1: Apply power of a product rule

$(2)^7 \cdot (x^8)^7$

Step2: Simplify constants and exponents

$128 \cdot x^{8 \times 7} = 128x^{56}$

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Problem 9: $(3n^8)^3$

Step1: Apply power of a product rule

$(3)^3 \cdot (n^8)^3$

Step2: Simplify constants and exponents

$27 \cdot n^{8 \times 3} = 27n^{24}$

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Problem 10: $(3x^4)^3$

Step1: Apply power of a product rule

$(3)^3 \cdot (x^4)^3$

Step2: Simplify constants and exponents

$27 \cdot x^{4 \times 3} = 27x^{12}$

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Problem 11: $(3b^8)^2$

Step1: Apply power of a product rule

$(3)^2 \cdot (b^8)^2$

Step2: Simplify constants and exponents

$9 \cdot b^{8 \times 2} = 9b^{16}$

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Problem 12: $(m^9n^3)^3$

Step1: Apply power of a product rule

$(m^9)^3 \cdot (n^3)^3$

Step2: Simplify exponents

$m^{9 \times 3} \cdot n^{3 \times 3} = m^{27}n^9$

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Problem 13: $(x^8y^5)^{10}$

Step1: Apply power of a product rule

$(x^8)^{10} \cdot (y^5)^{10}$

Step2: Simplify exponents

$x^{8 \times 10} \cdot y^{5 \times 10} = x^{80}y^{50}$

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Problem 14: $(yx^8)^3$

Step1: Apply power of a product rule

$(y)^3 \cdot (x^8)^3$

Step2: Simplify exponents

$y^3 \cdot x^{8 \times 3} = x^{24}y^3$

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Problem 15: $(x^8y^5)^8$

Step1: Apply power of a product rule

$(x^8)^8 \cdot (y^5)^8$

Step2: Simplify exponents

$x^{8 \times 8} \cdot y^{5 \times 8} = x^{64}y^{40}$

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Problem 16: $(3xy^8)^4$

Step1: Apply power of a product rule

$(3)^4 \cdot (x)^4 \cdot (y^8)^4$

Step2: Simplify constants and exponents

$81 \cdot x^4 \cdot y^{8 \times 4} = 81x^4y^{32}$

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Problem 17: $(2u^7v^5)^5$

Step1: Apply power of a product rule

$(2)^5 \cdot (u^7)^5 \cdot (v^5)^5$

Step2: Simplify constants and exponents

$32 \cdot u^{7 \times 5} \cdot v^{5 \times 5} = 32u^{35}v^{25}$

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Problem 18: $(3a^{10}b^4)^3$

Step1: Apply power of a product rule

$(3)^3 \cdot (a^{10})^3 \cdot (b^4)^3$

Step2: Simplify constants and exponents

$27 \cdot a^{10 \times 3} \cdot b^{4 \times 3} = 27a^{30}b^{12}$

Answer:

1. $16x^{20}$
2. $128x^{56}$
3. $27n^{24}$
4. $27x^{12}$
5. $9b^{16}$
6. $m^{27}n^9$
7. $x^{80}y^{50}$
8. $x^{24}y^3$
9. $x^{64}y^{40}$
10. $81x^4y^{32}$
11. $32u^{35}v^{25}$
12. $27a^{30}b^{12}$