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xz_007 [3.2K]
3 years ago
7

Which is the simplified form of the expression (6 to the power of -2 times 6 to the power of 5) to the -3rd power?

Mathematics
2 answers:
julsineya [31]3 years ago
7 0

Answer:

B. 1/6^9

Step-by-step explanation:

6^-2 = 1/6^2

1/6^2 * 6^5 = 6^5/6^2 = 6^3

6^(3 * -3) = 6^-9= 1/6^9

mr_godi [17]3 years ago
3 0

Answer:

<h2>B) 1 over (6 to the power of 9)</h2>

Step-by-step explanation:

\left(6^{-2}\cdot6^5\right)^{-3}\qquad\text{use}\ a^n\cdot a^n=a^{n+m}\\\\=(6^{-2+5})^{-3}=(6^3)^{-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=6^{(3)(-3)}=6^{-9}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{6^9}

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If 1st and 4tg terms of G.p are 500 and 32 respectively it's second term is ?
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Answer:

T_{2} = 200

Step-by-step explanation:

Given

Geometry Progression

T_1 = 500

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Required

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First, we need to write out the formula to calculate the nth term of a GP

T_n = ar^{n-1}

For first term: Tn = 500 and n = 1

500 = ar^{1-1}

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Make r^3 the subject

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r^3 = 0.064

Take cube roots

\sqrt[3]{r^3} = \sqrt[3]{0.064}

r  = \sqrt[3]{0.064}

r = 0.4

Using:  T_n = ar^{n-1}

n = 2     r = 0.4     and a = 500

T_{2} = 500 * 0.4^{2-1}

T_{2} = 500 * 0.4^1

T_{2} = 500 * 0.4

T_{2} = 200

<em>Hence, the second term is 200</em>

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