Repeated Exponentiation

Q. Simplify and write the answer in the exponential form.
${\left(4\right)}^{-3}\times {\left(5\right)}^{-3}\times {(-5)}^{-3}$
[2 marks]

Q. $a^m\times b^m$ would be equal to $(a\times b{)}^m$.

1. True
2. False

Q.

Find the value of ${625}^{\raisebox{1ex}{$-3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$

Q.

Fill in the blank to make the statement true:

${\left(\frac{-1}{4}\right)}^3\times {\left(\frac{-1}{4}\right)}^{\_\_}={\left(\frac{-1}{4}\right)}^{11}$

Q.

Write ${\left(ab\right)}^4$ in the expanded form.

Q. Which of the following option is equal to ${16}^3{a}^{12}\times {125}^4{b}^{12}?$

1. $(10ab{)}^{12}$
2. $10(ab{)}^{12}$
3. $(10{)}^{12}ab$
4. None of the above

Q. Tim wrote $7^2\times 7^4$ as $7^8$. Is he correct in this approach?

1. Yes
2. No

Q. The simplest form of ${27}^2\times 9^{-3}?$ is .

Q. What is the simplest form of the expression $(M^2{)}^{\frac{5}{6}}\times M^{\frac{1}{3}}$ ?

1. $M^{\frac{2}{3}}$
2. $M^{\frac{11}{6}}$
3. $M^2$
4. None of the above

Q. If $(a^3{)}^4=(a^6{)}^b,$ the value $b$ is .

Q. Evaluate the exponential expression $(-b{)}^4\times (-b{)}^2$, for $b=4$.

Q. Natasha says that $7^5$ is bigger than $5^7$. Has Natasha arrived at the right answer?

1. Yes
2. No
3. Cannot be determined

Q. Josie says that $-15$ when multiplied to itself 6 times gives $-{15}^6$ as the answer. Did she obtain the correct value?

1. True
2. False

Q.

Cube root of $8$ are $+2$ and $-2$.

1. True
2. False

Q. 8 when multiplied to 8 would give

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

Q.

Write the following in expanded form:-

$-4a^3{b}^2$

Q. Carl ate $3^5$ jelly beans and at the same time, Buffy ate $5^3$ jelly beans. Who ate more jelly beans?

1. Carl
2. Buffy
3. Both ate equally.
4. Cannot be determined.

Q.

ADDING AND SUBTRACTING IN SCIENTIFIC NOTATION

Find the sum or difference.

$(7.8\times {10}^7)–(2.45\times {10}^6)$

Q. Simplify the following expression such that the result has positive exponents: $\left(25M^2{N}^{-4}{)}^{1/2}\right(M^3{N}^{1/2}{)}^2$.

1. $5M^7/N$
2. $25M^5/N$
3. $5M^5/N$
4. $5M^6/N$

Q.

$3^7÷3^4=\_\_\_\_\_\_\_\_\_.$ $(3^{\frac{7}{4}}/3^{7-4})$

Q. Which of the following option is equal to $8^5?$

1. $2^8$
2. $5^8$
3. $2^{15}$
4. None of the above

Q.

ADDING AND SUBTRACTING IN SCIENTIFIC NOTATION

Find the sum or difference.

$(9.7\times {10}^6)+(6.7\times {10}^5)$

Q.

Find the value of $(-3)\times {(-2)}^3$.

Q. Select the exponent(s) which is(are) equal to $(a^m{)}^n.$

1. $a^{mn}$
2. $(a^n{)}^m$
3. $a^{m^n}$
4. $a^{n^m}$

Q.

${\left(x^m\right)}^n=\_\_\_\_\_\_$

Q. What would be the exponent of '$a^k$' in $a^k\times a^k\times a^k....$ (upto k times)?

1. $a$
2. $k$
3. $a\times k$
4. $a^k$