Powers and Exponents

Q. State the product law of exponents.

Q.

Write base and exponent in each of the following:

(i) $\frac{5}{7}$

Q. Simplify $\frac{5^{n+3}-6\times 5^{n+1}}{9\times 5^n-5^n\times 2^2}$

Q. If ${27}^x=\frac{9}{3^x},$ find x.

Q. If 2⁴ × 4² =16^x, then find the value of x.

Q. For what value of m is $x^2-2m{x}^2+16$ divisible by $x+2$?

Q.

Question 41

In the following question, fill in the blanks to make the statements true.

Very large lumbers can be expressed in standrad from using ___ exponents.

Q.

Question 40

In the following question, fill in the blanks to make the statements true.

Very small number can be expressed in standard from by using ___ exponents.

Q. Is $\sqrt{729}$ an example of a pure surd?

Q. If $a=3$ and $b=-2$, find the values of:$a^a+b^b$

Q. 7. Find factor-(3x)50-(5x)50 Where 50 is exponent

Q. When two numbers of n digits each are added and the sum occupies n + 1 digits, the situation is called-

1. None of these
2. Underflow
3. Normal condition
4. Overflow

Q. Express $10800$ in exponential form.

Q. Simplify:
$(x^{a+b}{)}^{a-b}.(x^{b+c}{)}^{b-c}.(x^{c+a}{)}^{c-a}$

Q. Write the value of $\sqrt[3]{7}\times \sqrt[3]{49}.$

Q. Construct a $△ABC$ in which $AB=5cm,BC=6cm\text{and}CA=7m.$

Q. solve: $\sqrt{\frac{(a^3-b^3{)}^5}{a^3-b^3}}$

1. $\left|\right(a^3+b^3{)}^2|$
2. $\left|\right(a^3-b^3{)}^2|$
3. $\left|\right(a^3-b^3{)}^3|$
4. $(a^3-b^3{)}^4$

Q. $As{O}_2^{2-}+Br{O}_3^{-}+H^{+}⟶B{r}^{-}+As{O}_4^{-}+H_{2}O$
Equivalent weight of $Br{O}_3^{-}=\frac{M}{x}$. The value of $x$ is :

Q. Evaluate the following:
${46}^3+{34}^3$

Q. Find the value of $(256{)}^{\frac{3}{4}}$.

Q. Find the value of $\sqrt[5]{516}\times \sqrt[5]{52}$. [1 Mark]

Q. A line is divided into three parts. The first part is two third the length of the second part. The third part is $\frac{1}{2}cm$ shorter than the first part and $2cm$ shorter than the second part. Find the length of the line?

1. $12cm$
2. $10cm$
3. $8cm$
4. $9cm$

Q. Write the set $G=\{9,16,25,36,...,81\}$ in set builder form.

1. $G=\{x|x=n^2,n\in N,3\le n<10\}$
2. $G=\{x|x=n^2,n\in N,3<n<10\}$
3. Data insufficient
   
4. None of these
   

Q. $\frac{a^2-b^2}{a-b}isequalto$

1. $(a-b{)}^2$
2. $a+b$
3. $a-b$
4. $a^2+b^2$