Product Rule of Exponents

Q.

Find the value of x, so that
${\left(\frac{5}{3}\right)}^{-2}\times {\left(\frac{5}{3}\right)}^{-14}={\left(\frac{5}{3}\right)}^{8x}$

1. -3

2. -2

3. -1

4. 0

Q. Solve for $x$ in the equation $(-5{)}^{x+1}\times (-5{)}^{-5}=(-5{)}^{-7}$.

1. -6
2. 4
3. 5
4. -3

Q.

Evaluate
${\left(\frac{5}{3}\right)}^2\times {\left(\frac{5}{3}\right)}^{14}$

1. ${\left(\frac{3}{5}\right)}^{12}$

2. ${\left(\frac{5}{3}\right)}^{16}$

3. ${\left(\frac{3}{5}\right)}^{16}$

4. ${\left(\frac{5}{3}\right)}^{-16}$

Q. Express the following expression as a product of prime factors only in exponential form: $729\times 64$

1. $3^3\times 2^2$
2. $3^6\times 2^6$
3. $6^3\times 6^2$
4. $2^3\times 3^2$

Q.

Express the following with a single exponent:

${\left(3^3\right)}^5\times {\left(3^4\right)}^2$

Q. Simplify and write the answer in exponential form:
$3^2\times 3^4\times 3^8$ [2 marks]

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. $x^5{y}^7$

Q. Solve for $x$ in the equation $(-5{)}^{x+1}\times (-5{)}^5=(-5{)}^7$.

1. 6
2. 7
3. 2
4. 1

Q. ${\left(2\right)}^5\times {\left(4\right)}^5={\left(24\right)}^5$.

1. True
2. False

Q.

Express ${\left(a^3\right)}^4$ with a single exponent.

Q.

Express the following with a single exponent:

${\left({10}^3\right)}^4\times {\left({10}^5\right)}^3$

Q.

Write in single exponent form:

${(-2)}^5\times b^5$

Q.

Express the following with a single exponent:

${\left(2^{10}\right)}^3\times {\left(2^5\right)}^4$

Q.

Write in the product form.

$x\times p^3$

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

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

Q.

Evaluate ${10}^{-1}\times {10}^3\times {10}^{-5}\times {10}^3$

1. 1

2. 10

3. 100

4. $\frac{1}{10}$

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.

Evaluate

$(\frac{a^m}{a^{-n}}{)}^{m-n}\times (\frac{a^n}{a^{-l}}{)}^{n-l}\times (\frac{a^l}{a^{-m}}{)}^{l-m}$

1. 0

2. a

3. 1

4. 2

Q. Solve for $x$ in the equation $3^{(2+x)}+3^{(1+x)}=2916.$

1. 4
2. 5
3. 6
4. 7

Q.

x^-a times x^-b = ?

1. x^{-(a + b)}

2. x^{-a + b}

3. x^{(a - b)}

4. x^-(a/b)