Question

[{1/2}^3 x {1/2}^4] divided by (1/8)^3

Answer 1

Question

Solve ⇒ $[\{ \frac{1}{2}\}^{3}\times \{\frac{1}{2}\}^{4}] \div (\frac{1}{8})^{3}$

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Answer

$[\{ \frac{1}{2}\}^{3}\times \{\frac{1}{2}\}^{4}] \div (\frac{1}{8})^{3}$

To solve this we need to apply laws of exponents. First we will solve brackets. In the brackets the bases are same so we will add the exponent to simplify. In simpler words we will use this law of exponent ⇒ $a^{m}\times a^{n} = a^{m+n}$

⇒ $[\{ \frac{1}{2}\}^{3}\times \{\frac{1}{2}\}^{4}] \div (\frac{1}{8})^{3}$

⇒ $[\{ \frac{1}{2}\}^{3+4}] \div (\frac{1}{8})^{3}$

⇒ $[\{ \frac{1}{2}\}^{7}] \div (\frac{1}{8})^{3}$

Now we will give the actual value to the numbers since no property can be applied here.

⇒ $[\{ \frac{1}{2}\}^{7}] \div (\frac{1}{8})^{3}$

⇒ $\frac{1}{128}\div \frac{1}{512}$

To divide these rational numbers we will find reciprocal of the divisor (i.e. second number) and multiply.

⇒ $\frac{1}{128}\div \frac{1}{512}$

⇒ $\frac{1}{128}\div \frac{512}{1}$

⇒ $\frac{512}{128}$

⇒ $4$

$\bf \therefore [\{ \frac{1}{2}\}^{3}\times \{\frac{1}{2}\}^{4}] \div (\frac{1}{8})^{3} = 4$

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