Multiplying Terms with Same Base

Q. If $a$ is a non-zero integer and $m$ is any integer, then $a^{-m}\times a^m$ = .

1. $1$
2. $0$
3. $a^{2m}$

Q. If $\frac{5^m\times 5^3\times 5^{-2}}{5^{-5}}=5^{12},$ then find m.

Q.

Obtain the product of

$2,4y,8y^2,16y^3$

Q. If $\frac{5^m\times 5^3\times 5^{-2}}{5^{-5}}=5^{12},$ then find m.

Q.

Observe the pattern carefully and fill in the blanks.

$752387533875438\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Q. The exponent of the product a^m x a^ n is ___.

1. m-n
2. m+n
3. mn
4. m/n

Q. If $\frac{5^m\times 5^3\times 5^{-2}}{5^{-5}}=5^{12},$ then find m.

Q. What should be the value of $x$, such that it satisfies the equation $4^x=\frac{\sqrt{16}}{256}$ ?

1. 3
2. -3
3. 4
4. 2

Q. If $4^x-4^{x-1}=48$, then $(2x{)}^x$ equals

1. $216$
2. $156$
3. $64$
4. $125$

Q.

The value of $m$ which satisfies $(2{)}^{m+1}\times 2^5=4^{-2}$ is:

___

Q.

Question 68

State whether the following statement is true or false:

If x and y are integers such that $x^2>y^2$, then $x^3>y^3$

Q. The value of x from the equation
$\sqrt{x^2+2x-3}+\sqrt{x^2-x}=\sqrt{5(x-1)}$ will be ____________.

1. $\{1,\frac{1}{5}\}$
2. $\{\frac{1}{5},\frac{1}{3}\}$
3. $\{1,-\frac{1}{5}\}$
4. $\{\frac{1}{2},\frac{1}{5}\}$

Q.

An algebraic fraction is being given as $4\times \left(\frac{(2-\frac{(m+n)}{(m-n)})}{\frac{(m-3n)}{(m-n)}}\right)$. What is the decimal value of this expression?

1. 2

2. 3

3. 4

4. 1

Q. lf $(7+4\sqrt{3}{)}^{x^2-8}+(7-4\sqrt{3}{)}^{x^2-8}=14$, then $x$ is

1. $3,\sqrt{7}$
2. $\pm 3,\pm 1$
3. $\pm 3;\pm \sqrt{7}$
4. $\pm 3,\pm 4$

Q. Evaluate
${\left(53\right)}^{-2}\times {\left(53\right)}^{-14}$

1. ${\left(53\right)}^{-16}$
2. ${\left(53\right)}^{16}$
3. ${(-53)}^{16}$
4. ${\left(-53\right)}^{-16}$

Q.

Find the value of the following: ${(-2)}^2\times {(-1)}^2$

Q.

When multiplying terms with the same base, the exponents are ____.

1. divided

2. subtracted

3. added

4. multiplied

Q. If $2^x-2^{x-1}=4$, then $x^x$ is equal to

1. $7$
2. $27$
3. $3$
4. None of the above

Q.

Write in the product form.

$17x^3{y}^4$

Q. Find the value of $\frac{{10}^{22}+{10}^{20}}{{10}^{20}}$.

1. $10$
2. ${10}^{42}$
3. ${10}^2$
4. $101$

Q.

Find the value of $m$ if $(-10{)}^{m+1}\times (-10{)}^5=(-10{)}^7.$

1. 1

2. 2

3. 3

4. -1

Q. If $\frac{2^m\times 2^4\times 2^{-6}}{2^{-5}}=2^{10}$, then $m$ = ___.

1. -3
2. 7
3. 10
4. 17

Q. Simplify: $x^2\times y^2\times x^5\times y^3$

1. $x^7{y}^5$
2. $x^7{y}^7$
3. $x^5{y}^5$
4. $x^5{y}^7$

Q.

The value of (5)^(4) x (5)^(5) is

1. 1/5

2. (5)^(4)

3. (5)^(6)

4. (5)^(9)

Q. $2^{-5}\times 2^{-10}$ =

1. $2^{-15}$
2. $2^{15}$
3. $2^{-5}$
4. $2^5$

Q.

Write in the product form.

$18x^9{y}^8{z}^6$

Q. If $\frac{5^m\times 5^3\times 5^{-2}}{5^{-5}}=5^{12},$ then find m.

Q.

Write in single exponent form:

$6^4\times {10}^4$

Q.

Multiply : $-17\mathrm{p}+18\mathrm{a}$ by $2$

Q. The sum of the first $n-$terms of the series $1^2+{2.2}^2+3^2+{2.4}^2+5^2+{2.6}^2+.........$ is, when $n$ is even. When $n$ is odd, the sum is

1. $\frac{n{(n+1)}^2}{4}$
2. $\frac{n^2(n+2)}{4}$
3. $\frac{n^2(n+1)}{4}$
4. $\frac{n{(n+2)}^2}{4}$