Question

Write 1458 and 1176 in exponential form

Answer 1

(i) First, we need to do prime factorization.

$\begin{array}{r | l} 2 & 1458 \\ \cline{2-2} 3 & 729 \\ \cline{2-2} 3 & 243 \\ \cline{2-2} 3 & 81 \\ \cline{2-2} 3 & 27 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \\ \end{array}$

The product of primes is ⇒  

$2\times 3\times3\times3\times3\times3\times3$

So therefore 1458 in exponential form would be ⇒ $2\times3^{6}$.

(ii) First, we need to do prime factorization.

$\begin{array}{r | l} 2 & 1176 \\ \cline{2-2} 2 & 588 \\ \cline{2-2} 2 & 294 \\ \cline{2-2} 3&147 \\ \cline{2-2}7 &49 \\ \cline{2-2} 7 &7 \\ \cline{2-2} & 1 \\ \end{array}$

The product of primes is ⇒  

$2 \times 2 \times 2 \times 3 \times 7 \times 7$

So therefore 1458 in exponential form would be ⇒ $2^{3}\times3\times7^{2}$.

Additional Information ❤

What is an exponent?

A number that says how many times to use the number in multiplication is known as exponent.

For example ⇒

In 2², the "2" says to use 2 twice in a multiplication.

So, 2² = 2×2 = 4

How to pronounce a number with exponent?

For example ⇒ 7²

We pronounce it as "7 raised to the power 2" or "7 square".

What are the exponent's laws?

• $a^{m}\times a^{n}=a^{m+n}$

• $\frac{a^{m}}{a^{n}} = a^{m}\div a^{n} = a^{m-n}$

• $a^{m}\times b^{m} = (ab)^{m}$

• $a^{m}\div b^{m}=( \frac{a}{b})^{m}$

• $(a^{m})^{n}=a^{m\timesn}$

• $(\frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$

• $a^{0}=1$

• $a^{-m}=\frac{1}{a^{m}}$

• $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$

Answer 2

Step-by-step explanation:

First we have to do prime factorisation

2|1458

3|729

3|243

3|81

3|27

3|9

3|3

|1

then the product of 1458 is 2×3×3×3×3×3×3

so therefore 1458 in exponential form would be

2×3 with power 6