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3 years ago

9

When he was measuring herbs on his balance scale, Neville placed a 1/2 gram weight, then a 1/5 gram weight, and finally a 1/8 gr

am weight before the scale balanced. How much did his herbs weigh?

1 answer:

Delvig [45]3 years ago

8 0

Answer: $\dfrac{33}{40}\ gm$

Step-by-step explanation:

Given

Neville place three weights in the sequence

$\dfrac{1}{2}\ gm,\dfrac{1}{5}\ gm,\dfrac{1}{8}\ gm$

The total weight of the three weights is

$\Rightarrow \dfrac{1}{2}+\dfrac{1}{5}+\dfrac{1}{8}=\dfrac{20+8+5}{40}\\\\\Rightarrow \dfrac{33}{40}\ gm$

Thus, herbs weigh $\frac{33}{40}\ gm$

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Prove the divisibility:<br><br>45^45·15^15 by 75^30

garri49 [273]

Answer:

$3^{75}$ .

Step-by-step explanation:

We have been an division problem: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

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Substituting these values in our division problem we will get,

$\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}$

$\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

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Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

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Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{105}}{3^{30}}=3^{105-30}$

$3^{105-30}=3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

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