Laws of Exponents

Q.

$Findthevalueof({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}$ .

1. 

2. 

3. 

4. 

Q. Tick (✓) the correct answer:
If $\left(x-\frac{1}{x}\right)=6$, then $\left(x^2+\frac{1}{x^2}\right)=?$
(a) 36
(b) 38
(c) 32
(d) $36\frac{1}{36}$

Q.

If $a^m$ × $a^n$ = $a^x$ (where m and n are natural numbers), then the value of $x$ is _____.

1. mn

2. m + n

3. m - n

4. 

Q. Evaluate : a) (1007)³ b) 5.05 × 5.05 × 5.05 - 0.05 × 0.05 × 0.05 / 5.05 × 5.05 + 5.05 + 0.05 × 0.05 c) (x - 2y)³ - (x + 2y)³

Q. Simplify and express in exponential form:

$\left[\right(5^2{)}^3\times 5^4]÷5^7$ [3 MARKS]

Q.

$x^m\times x^n=\_\_\_\_\_\_$

Q.

Which of the following are not true?

i) $3^{\left(\frac{1}{3}\right)}$ = $\sqrt{3^{-3}}$
ii) $3^{\left(\frac{1}{2}\right)}$ = $\sqrt{3^2}$
iii) $3^{-2}$ = $\sqrt{3}$
iv) $3^{\left(\frac{1}{2}\right)}$ = $\sqrt{3}$

1. i, ii, iii

2. ii, iii, iv

3. i, ii,

4. iii, iv

Q.

In the following, you are given the product pq and the sum p + q, Determine p and q:

(i) pq = 18 and p + q = 11; (ii) pq = 32 and p + q = − 12; (iii) pq = − 24 and p + q = 2; (iv) pq = − 12 and p + q = 11; (v) pq = − 6 and p + q = − 5; (vi) pq = − 44 and p + q = − 7.

Q.

Factorise the following expressions

(i) p² + 6p + 8

(ii) q² − 10q + 21

(iii) p² + 6p − 16

Q.

Simplify and express in exponential form:
$4^3$ x $4^{-2}$ x ${16}^2$

1. 4³

2. 4⁵

3. 4⁶

4. 4⁴

Q.

What is the value of $\sqrt[3]{38}$ + $\frac{1}{\sqrt[3]{38}}$ ?

1. 2

2. 2.5

3. 0.5

4. 1

Q.

Work out the following divisions.

(i) (10x − 25) ÷ 5

(ii) (10x − 25) ÷ (2x − 5)

(iii) 10y(6y + 21) ÷ 5(2y + 7)

(iv) 9x²y²(3z − 24) ÷ 27xy(z − 8)

(v) 96abc(3a − 12)(5b − 30) ÷ 144(a − 4) (b − 6)

Q.

State true or false:
The value of ($4^{-7}$ ÷ $4^{-10}$ ) × $4^{-5}$ is ${16}^{-1}$.

1. False

2. True

Q.

$\frac{\left(a^m\right)\times \left(a^n\right)}{\left(a^p\right)}$ can be rewritten as:

1. $a^{m+n-p}$

2. $a^{m-p-n}$

3. $a^{n-p-m}$

4. $a^{p-m+n}$

Q. Tick (✓) the correct answer:
If $\frac{4x+8}{5x+8}=\frac{5}{6},$ then x = ?
(a) 4
(b) 6
(c) 8
(d) 12

Q.

The value of the expression ${\left(\right(2{)}^2)}^2$× ($3^3$ ÷$4^2$) ÷ $3^2$ is equal to:

1. 3

2. 27
3. $\frac{13}{3}$

4. 1

Q.

$4^{-2}+4^{-1}+4^0+4^2$ = ___.

1. $\frac{277}{16}$

2. $\frac{277}{18}$

3. $\frac{257}{16}$
4. $\frac{271}{18}$

Q. Find the cube-roots of 2.744

Q. Question 5
Find the value of m for which
$5^m÷5^{-3}=5^5$

Q.

Find and correct the errors in the statement: (a + 4) (a + 2) = a² + 8

Q.

Question 114

The number of red blood cells per cubic millimeter of blood is approximately 5.5 million. If the average body contains 5 L of blood what is the total number of red cells in the body? Write the standard form.
$(1L=1000000m{m}^3)$

Q.

Evaluate the exponential expression $x^5$ × $x^4,forx=2$.

1. 32

2. 128

3. 512

4. 256

Q. Tick (✓) the correct answer:
If $z=\frac{4}{5}(z+10),\mathrm{then}z=?$
(a) 40
(b) 20
(c) 10
(d) 60

Q.

Simplify: ${(2^5÷2^8)}^5$ × $2^{-5}$

1. 1/2¹⁰

2. 1/2²⁰

3. 1/2^(-15)

4. 1/2^(-5)

Q.

Divide as directed.

(i)$5(2x+1)(3x+5)÷(2x+1)$

(ii)$26xy(x+5)(y-4)÷13x(y-4)$

(iii)$52pqr(p+q)(q+r)(r+p)÷104pq(q+r)(r+p)$

(iv)$20(y+4)(y^2+5y+3)÷5(y+4)$

(v)$x(x+1)(x+2)(x+3)÷x(x+1)$

Q. Tick (✓) the correct answer:
If $\frac{n}{n+15}=\frac{4}{9}$, then n = ?
(a) 4
(b) 6
(c) 9
(d) 12

Q. Find the value of using the column method:
(52)²

Q. Mark (✓) against the correct answer:
3 + 23x − 8x² = ?
(a) (1 − 8x)(3 + x)
(b) (1 + 8x)(3 − x)
(c) (1 − 8x)(3 − x)
(d) none of these

Q. The value of the expression ${\left(\right(2{)}^2)}^2$× ($3^3$ ÷$4^2$) ÷ $3^2$ is equal to:

Q.

(a) Simplify 3x (4x −5) + 3 and find its values for (i) x = 3, (ii) .

(b) a (a² + a + 1) + 5 and find its values for (i) a = 0, (ii) a = 1, (iii) a = − 1.