Exponents with like Bases

Q.

If $5^{2x+1}÷25=125$, find the value of x.

Q.

If ${\left[{\left\{{\left(\frac{1}{7^2}\right)}^{-2}\right\}}^{-\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m$ then find the value of $m$.

1. $-\frac{1}{3}$

2. $\frac{3}{2}$

3. $-\frac{1}{7}$

4. $\frac{2}{8}$

Q.

If $2^x=4^y=8^z$ and $\frac{1}{2x}+\frac{1}{4y}+\frac{1}{4z}=4$, find the value of $x$.

Q. If ${\left[{\left\{{\left(\frac{1}{7^2}\right)}^{-2}\right\}}^{-\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m$ then find the value of m.

1. $-\frac{1}{3}$
2. $\frac{2}{8}$
3. $-\frac{1}{7}$
4. $\frac{3}{2}$

Q.

Question 3(ii)
Find the value of:

$(2^{-1}\times 4^{-1})÷2^{-2}$

Q.

Find the value of x for which ${\left(\frac{5}{3}\right)}^{-4}\times {\left(\frac{5}{3}\right)}^{-5}={\left(\frac{5}{3}\right)}^{3x}$

Q.

If ${\left(\sqrt{\frac{3}{5}}\right)}^{x+1}=\frac{125}{27}$ find the value of $x$

Q.

Simplify :

$\left(i\right)\frac{a^{2n-3}.a^{(2n+1)(n+2)}}{{\left(a^3\right)}^{2n+1}.a^{n(2n+1)}}\left(ii\right)\frac{x^{2n+7}.{\left(x^2\right)}^{3n+2}}{x^{4(2n+3)}}$

Q.

Evaluate :

$\left(i\right)(3^{-1}\times 9^{-1})÷3^{-2}\left(ii\right)(3^{-1}\times 4^{-1})÷6^{-1}\left(iii\right)(2^{-1}+3^{-1}{)}^3(iv\left)\right(3^{-1}÷4^{-1}{)}^2\left(v\right)(2^2+3^2)\times {\left(\frac{1}{2}\right)}^2\left(vi\right)(5^2-3^2)\times {\left(\frac{2}{3}\right)}^{-3}\left(vii\right)[{\left(\frac{1}{4}\right)}^{-3}-{\left(\frac{1}{3}\right)}^{-3}]÷{\left(\frac{1}{6}\right)}^{-3}\left(viii\right){\left[{(-\frac{3}{4})}^{-2}\right]}^2\left(ix\right){\left\{{\left(\frac{3}{5}\right)}^{-2}\right\}}^{-2}\left(x\right)(5^{-1}\times 3^{-1})÷6^{-1}$

Q.

Find the value of x for which ${\left(\frac{4}{9}\right)}^4\times {\left(\frac{4}{9}\right)}^{-7}={\left(\frac{4}{9}\right)}^{2x-1}$

Q.

If a + b + c = 0, then ($a^3$ + $b^3$ + $c^3$) is equal to-

1. abc

2. 0

3. 3abc

4. (ab + bc + ca)

Q.

The value of x for which ${\left(\frac{7}{12}\right)}^{-4}\times {\left(\frac{7}{12}\right)}^{3x}={\left(\frac{7}{12}\right)}^5$ is

(a)-1

(b) 1

(c) 2

(d) 3

Q.

Question 2(i)
Simplify and express the result in power notation with positive exponent:

$(-4{)}^5÷(-4{)}^8$

Q.

The exponent of $3$ in $100!$ is?

1. $33$

2. $44$

3. $48$

4. $52$

Q.

Simplify: $7^{\frac{1}{2}}\times 8^{\frac{1}{2}}$.

Q. Find the value of x, if

(i) $3^x=81$

(ii) $2^{x-3}=1$

(iii) $3^{3x-5}=\frac{1}{9^x}$ [4 MARKS]

Q. If $a$ is a non-zero integer and $m$ and $n$ are any integers, then $a^m\times a^n$ = .

1. $a^{mn}$
2. $a^{m+n}$
3. $a^{\frac{m}{n}}$

Q.

Question 69

Find $m$, so that ${\left(\frac{2}{9}\right)}^3\times {\left(\frac{2}{9}\right)}^6={\left(\frac{2}{9}\right)}^{2m-1}$

Q.

The middle term in the expansion of ${\left[x-\frac{1}{x}\right]}^{18}$ is

1. ${}^{18}C_9$

2. $-{}^{18}C_9$

3. ${}^{18}C_{10}$

4. $-{}^{18}C_{10}$

Q.

Find the value of the following expression:

${\left(\frac{256}{625}\right)}^{-1/2}$

Q.

Write the following numbers in the expanded from with exponential notation:

$23,89,010$

Q.

Find x, if

$\left(i\right){\left(\frac{1}{4}\right)}^{-4}\times {\left(\frac{1}{4}\right)}^{-8}={\left(\frac{1}{4}\right)}^{-4x}\left(ii\right){\left(\frac{-1}{2}\right)}^{-19}÷{\left(\frac{-1}{2}\right)}^8={\left(\frac{-1}{2}\right)}^{-2x+1}\left(iii\right){\left(\frac{3}{2}\right)}^{-3}÷{\left(\frac{3}{2}\right)}^5={\left(\frac{3}{2}\right)}^{2x+1}\left(iv\right){\left(\frac{2}{5}\right)}^{-3}\times {\left(\frac{2}{5}\right)}^{15}={\left(\frac{2}{5}\right)}^{2+3x}\left(v\right){\left(\frac{5}{4}\right)}^{-x}÷{\left(\frac{5}{4}\right)}^{-4}={\left(\frac{5}{4}\right)}^5\left(vi\right){\left(\frac{8}{3}\right)}^{2x+1}\times {\left(\frac{8}{3}\right)}^5={\left(\frac{8}{3}\right)}^{x+2}$

Q.

Simplify and reduce to a simple fraction: $\left(\frac{4}{5}\right)÷\left(\frac{7}{15}\right)\times \left(\frac{8}{9}\right)$

Q.

Simplify ${(2^5÷2^8)}^5$ × $2^{-5}.$

1. $\frac{1}{2^{10}}$

2. $\frac{1}{2^{20}}$

3. $\frac{1}{2^{(-15)}}$

4. $\frac{1}{2^{(-5)}}$

Q.

Question 180(v)

Simplify

$\frac{(9{)}^3\times 27\times t^4}{(3{)}^{-2}\times (3{)}^4\times t^2}$

Q.

If $a^{n+2}$ = $a^{2n-1},$ then the value of $n$ is __.

1. 0

2. 3

3. 2
4. 1

Q.

Question 119

Find the value of n.
$\frac{2^n\times 2^6}{2^{-3}}=2^{18}$

Q.

Question 1(i)
Find the value of:
(i) $2^6$

Q.

Evaluate:

$\left(i\right)(\frac{5}{3}{)}^2\times (\frac{5}{3}{)}^2$

$\left(ii\right)(\frac{5}{6}{)}^6\times (\frac{5}{6}{)}^{-4}$

$\left(iii\right)(\frac{2}{3}{)}^{-3}\times (\frac{2}{3}{)}^{-2}$

$\left(iv\right)(\frac{9}{8}{)}^{-3}\times (\frac{9}{8}{)}^2$

Q.

Simplify: $x^2{y}^2{x}^5{y}^3$

1. $x^7{y}^5$

2. $x^7{y}^7$

3. $x^5{y}^5$

4. $x^5{y}^7$