For example: (i) \(7^3\)
By evaluating, we get:
\(7^3=7×7×7\)
\(=49×7\)
\(=343\)
(ii) \(10^3\)
By evaluating, we get:
\(10^3=10×10×10\)
\(10^3=1000\)
For example: \(6^2+4^3\)
First, we will evaluate the exponents
\(=36+64\)
Now, we will add
\(=100\)
Thus, \(6^2+4^3=100\)
For example:
\(2^3.3^2\)
First, we will evaluate the exponents.
\(=2×2×2×3×3\)
\(=8×9\)
Now, we will multiply
\(=72\)
Thus, \(2^3.3^2=72\)
For example: \(\dfrac{4^2}{2^4}\)
First, simplify the exponents.
Multiples of 4 = 1, 2 and 4
So we can write,
\(\dfrac{4^2}{2^4}=\dfrac{(2×2)^2}{{2}^4}\)
Using the property \((x.y)^a=x^a.y^a\)
\(=\dfrac{2^2×2^2}{2^4}\)
\(=\dfrac{{2}^{(2+2)}}{{2}^4}\) \(\Bigg[\because\, x^a.x^b=x^{a+b}\Bigg]\)
\(=\dfrac{2^4}{2^4}\)
Now, divide
\(=1\)
Thus, \(\dfrac{4^2}{2^4}=1\)
For example: \(8^3-36\)
First, we will evaluate the exponent
\(=512-36\)
Now, we will subtract
\(=476\)
Thus, \(8^3-36=476\)
> Greater than
< Less than
= Equal to
Case 1: When the base is same but the power is different.
For example: \((4)^2\text{_____}(4)^3\)
Since the base is same, so we will compare the powers.
We know that \(2<3\)
Thus,
\((4)^2<(4)^3\)
Hence, when the base is same but the power is different, then the number with larger power is greater.
Case 2: When the power is same but the base is different.
For example: \((5)^3\text{_____}(10)^3\)
Since the power is same, so we will compare the bases.
We know that \(5<10\)
Thus, \((5)^3<(10)^3\)
Hence, when the power is same but the base is different, then the number with larger base is greater.
Case 3: When both base and power are different.
For example: \((5)^3\text{_____}(6)^2\)
First, we will evaluate the terms.
\(5^3=5×5×5=125\)
\(6^2=6×6=36\)
Now, we will rewrite the numbers and compare them.
\(125>36\)
Hence, when both power and base are different, we first evaluate each exponent and then compare them.
Note: The opening of the symbol is always towards the larger number.
A \(35\)
B \(5\)
C \(3\)
D \(1\)