Exponents with Unlike Bases and Same Exponent

Q.

Simplify ${\left(\frac{81}{16}\right)}^{-\frac{3}{4}}\times \left[{\left(\frac{25}{9}\right)}^{-\frac{3}{2}}÷{\left(\frac{5}{2}\right)}^{-3}\right]$

Q.

1024 is ______ power of 4.

1. 2nd

2. 3rd

3. 4th

4. 5th

Q.

Express $3.02\times {10}^{-6}$ in the usual form.

Q.

If $2^{10}+2^9\times 3^1+2^8\times 3^2+....2\times {10}^9+3^{10}=S-2^{11}$, then $S$ is equal to

1. $3^{11}$

2. $\frac{3^{11}}{2}+2^{10}$

3. $2\times 3^{11}$

4. $3^{11}-2^{12}$

Q.

Question 73

Find the value of $n$, where $n$ is an integer and $2^{n-5}\times 6^{2n-4}=\frac{1}{{12}^4\times 2}.$

Q.

Simplify :${25}^{\frac{3}{2}}$

Q.

Simplify: ${\left\{{81}^{-3/4}\times \frac{{16}^{1/4}}{6^{-2}}\times {\left(\frac{1}{27}\right)}^{-4/3}\right\}}^{1/3}$

Q.

Question 1(ii)
Find the value of:
(ii) $9^3$

Q.

Question 85 (a)

Evaluate
$\frac{7^8\times a^{10}{b}^7{c}^{12}}{7^6\times a^8{b}^4{c}^{12}}$

Q. Simplify
${13}^{\frac{1}{5}}\times {17}^{\frac{1}{5}}$

Q. Question 1(x)
Using laws of exponents, simplify and write the answer in exponential form:
(x) $8^t÷8^2$

Q.

if $4^4+4^4+4^4+4^4=4^a$ , then $a=$___

Q.

Simplify and write the following in exponential form : ${\left(3^4\right)}^{-3}-2^0\times {\left(3^2\right)}^4+{\left(2^0\right)}^2$ .

Q.

Write an expression that simplifies to ${\mathrm{x}}^{24}$ using the Power of a Power Property.

Q.

Question 6(iv)
Simplify:
(iv) $3\times 4^4$

Q. Find the value of $2^6$

Q.

Question 2(vi)
Express the following in exponential form:
(vi) $a\times a\times a\times c\times c\times c\times c\times d$

Q. Simplify: $\frac{3^5\times {10}^5\times 25}{5^7\times 6^5}$

Q.

Find the product by suitable rearrangement.

$8\times 291\times 125$

Q.

${\left(\frac{2}{3}\right)}^3\times {\left(\frac{5}{7}\right)}^3$ is equal to

$\left(a\right){(\frac{2}{3}\times \frac{5}{7})}^9$
$\left(b\right){(\frac{2}{3}\times \frac{5}{7})}^6$
$\left(c\right){(\frac{2}{3}\times \frac{5}{7})}^3$
$\left(d\right){(\frac{2}{3}\times \frac{5}{7})}^0$

Q.

State true or false.
$\frac{1}{0}$ is a defined quantity.

1. False

2. True

Q. Simplify
${64}^{-\frac{1}{3}}\times [{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}]$.

Q.

Using laws of exponents, simplify and write the answer in exponential form:

(ii) $p^3\times p^2$

Q. Simplify:
$\frac{3^{30}+3^{29}+3^{25}}{3^{31}+3^{30}-3^{29}}+\frac{2^{30}+2^{29}+2^{25}}{2^{31}+2^{30}-2^{29}}$

Q. Simplify:
$\frac{{\left(15\right)}^{-3}\times {(-12)}^4}{5^{-6}\times {36}^2}$

Q.

Simplify the following and write the answer in the exponential notation.

${\left(5^3\right)}^7$

Q.

The value of $(3^0-2^0)\times 5^2$ is:

1. 1

2. 25

3. 0

4. 9

Q.

Find the value of $(\frac{2}{3}{)}^5\times 3^6\times \frac{1}{8}\times \frac{1}{6}$.
___

Q.

Find the value of $4^3\times 2^3$.
Ans: ___

Q. Simplify: $\frac{3^5\times {10}^5\times 25}{5^7\times 6^5}$