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10) The statement is TRUE.
82  87
 74
3
8
 
2
 6.03  106
Let us break this expression down into two parts separated by the “+” sign.
Consider the first part of this expression:
82  87

3
8
The same base value of 8 is used throughout this part and so we can use the rules of indices.
Two rules of indices are helpful here.
(i) To multiply powers of the same base add the indices:
am  an  am n
(ii) To divide powers of the same base subtract the indices:
am
 amn
n
a
Applying rule (i) (with a=8, m=2, n=7) we get:
82  87 82  7 89
 3  3
83
8
8
Next we apply rule (ii) (now with a=8, m=9, n=3) to get:
82  87 89
 3  89 3  86
3
8
8
You can also check your answer, and improve your understanding of the rules of indices, by
using the definition of indices to write out the expression in full and then cancel down:
82  87 /8 /8  /8  8  8  8  8  8  8

3
/8  8/ /8
8
 88 8 88 8
 86
Now we need to consider the second part of the expression:
7 
4 2

Another rule of indices is helpful here.
(iii) To raise a power of a quantity to a power, multiply the indices:
a 
m n
 a m n
Applying rule (iii) (now with a=7, m=4, n=2) we get:
7 
4 2
 742  78
Again, you can also check your answer, and improve your understanding of the rules of
indices, by using the definition of indices to write out the expression in full:
7 
4 2
 74  74
 7  7  7  7 7  7  7  7
 78
Piecing together both parts of the expression gives us the following simplified expression:
82  87
4

7
83
 
2
 86  78
The right-hand-side cannot be simplified further since each term has a different base value (8
and 7, respectively).
On your calculator, look out for the following keys , x2, 3, x3, x, x
associated with finding powers and roots.
or ^ or xy which are
[]
On the CASIO fx-85GT calculator,
is the square root key (use SHIFT and this key
for cube root), and to raise a number to a power you can use the
key (use SHIFT and
[]
x
this key for roots).
Both these keys are on the third row from the top.
is the second key in from the left, and moving two keys to the right takes us to x [] .
[]
(Note: When either of these keys is pressed, an open bracket “(” appears on the screen and so
we need to press the “)” key to close the bracket. Note too that the screen displays “raising to
the power” as “^” when the
key is pressed).
[]
x
For this question we press the following 10 keys:
8
x []
6
)
+
7
x []
Your calculator should report the answer as:
6026945
8
)
=
You might also like to check you get the same answer when you key in the original left-handside:
x []
x []
8
2
)
7
)

8
)
x [] 3
8

+
(
7
x []
4
)
)
x []
2
)
=
Your calculator should report the same answer, i.e.:
6026945
Note that the original left-hand-side uses 25 keys compared to the 10 key simplified version
above. Having this many more keys to press in the key sequence greatly increases the risk of
an error occurring!
Since 6026945 is a large number we can use standard form to write it more neatly as:
6.03  106
(to 2 decimal places).
To change a whole number to standard form, put a decimal point after the first digit and count how
many digits are left – this gives the power of 10.
e.g.
1 385 = 1.385 × 103
1 385 000 000 000 = 1.385 × 1012
To change a decimal to standard form, put a decimal point after the first non zero digit and count
how many digits there are from the original position of the point to the new position – this gives the
negative power of 10.
e.g.
0.000789 = 7.89 × 10-4
On the CASIO fx-85GT calculator, the result of a calculation will automatically be displayed
in exponential display format if the number has too many digits to fit on the display. To enter
a number in standard form use the key,
located in the middle of the bottom row.
x
x10
(Other calculators, e.g. older models, may have an EXP key to use instead.)
To key in
6.03  106
press the following key sequence:
6
.
0
3
x10 x
6
To add or subtract numbers in standard form, convert back to ordinary numbers to do the
calculation.
To multiply or divide numbers in standard form, use the ordinary rules of indices.